Both of those part numbers are for the same memory. CT1124872 is CT51264AC800 when you order it against the HP G71-340US model. Both are guaranteed to be compatible with that model. You can see it listed against that system here: http://www.crucial.com/usa/en/hp-g71-340us/CT1124872
We do also have a great guide and support section on our website. This has different installation guides and support on how to install your memory. You can see that on our website here: http://www.crucial.com/usa/en/support-memory
Please enjoy your upgrade and if you do have any other questions at all, please don't hesitate to ask.